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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details)
$ in Thousands
 3 Months Ended
Dec. 31, 2021
USD ($)
segment
country
Jan. 01, 2021
USD ($)
Oct. 01, 2021
USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Number of reportable segments | segment 3    
Cash and cash equivalents $ 415,467   $ 532,591
Equity method investment, aggregate cost 279,200   224,600
Equity securities without readily determinable fair value, amount 180,500   180,500
Deferred income taxes and other liabilities 1,014,155   1,079,014
Deferred Income Taxes and Other Noncurrent Liabilities | CARES Act      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Payment of deferred social security taxes 64,200    
Deferred income taxes and other liabilities 64,200    
Uniform | Cost of services provided      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
CARES Act. COVID-19 labor related credit   $ 4,700  
FSS United States and Uniform | Cost of services provided      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
CARES Act. COVID-19 labor related credit 12,200 $ 35,100  
Captive      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Cash and cash equivalents $ 178,900   $ 194,300
Foreign Countries Outside North America      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Number of foreign countries in which entity operates | country 18